The following signals from impedance relays can, in general, be applied for fault location: phasors and/or amplitudes of relaying currents/voltages, which are composed for measurement of apparent impedance of fault loops, phasors of particular sequence components of phase currents and voltages, and measured apparent impedances of fault loops “seen” from the line terminals.
Utilization of measurements from impedance relays for fault location has been initiated by M. Sachdev and Agarwal in the papers “Accurate fault location estimates from digital impedance relay measurements,” Proceedings of Third International Conference on Developments in Power System Protection, London, 17-19 Apr. 1985, Conference Publication No. 249, pp 180-184 (paper [1]) and “A technique for estimating transmission line fault locations from digital impedance relay measurements,” IEEE Transaction on Power Delivery, Vol. 3, No. 1, January 1988, pp 121-129 (paper [2]). Their method uses the following measurements from impedance relays installed at both the line terminals:                for single phase-to-ground faults: apparent impedances of fault loops, phasors of relaying currents and phasors of a zero sequence current,        for the other fault types: apparent impedances of fault loops, phasors of a positive and a negative sequence currents.        
The method presented in papers [1-2] uses Cartesian description of the relations between the input data for different fault types. In consequence, in papers [1-2] a rather complex fault location algorithm is obtained. The algorithm contains 28 steps to be performed in a sequence dependent on a fault type.
In the method of the papers [1-2] the synchronization angle is required to be calculated. The calculations of the synchronization angle proposed in papers [1-2] are based on solving a quadratic equation for the unknown angle. As always for quadratic equations, two solutions are obtained. A specific one of them is taken further. Generally this provides the correct fault location in huge majority of the cases. However, there is no proof in papers [1-2] that this works correctly in complex configurations of transmission networks and different specifications of a fault. Further, the algorithm of the papers [1-2] is derived for a single line only, and subsequently can not handle parallel lines.